The Nash Equilibrium Revisited: Chaos and Complexity Hidden in Simplicity

The Nash Equilibrium is a much discussed, deceptively complex, method for the analysis of non-cooperative games. If one reads many of the commonly available definitions the description of the Nash Equilibrium is deceptively simple in appearance. Modern research has discovered a number of new and important complex properties of the Nash Equilibrium, some of which remain as contemporary conundrums of extraordinary difficulty and complexity. Among the recently discovered features which the Nash Equilibrium exhibits under various conditions are heteroclinic Hamiltonian dynamics, a very complex asymptotic structure in the context of two-player bi-matrix games and a number of computationally complex or computationally intractable features in other settings. This paper reviews those findings and then suggests how they may inform various market prediction strategies.Comment: 13 Pages, 5th International Conference on Complex System

The Symmetries and Redundancies of Terror: Patterns in the Dark, A study of Terrorist Network Strategy and Structure

Although much political capital has been made regarding the war on terrorism, and while appropriations have gotten underway, there has been a dearth of deep work on counter-terrorism, and despite massive efforts by the federal government, most cities and states do not have a robust response system. In fact, most do not yet have a robust audit system with which to evaluate their vulnerabilities or their responses. At the federal level there remain many unresolved problems of coordination. One reason for this is the shift of much of federal spending on war-fighting in Afghanistan and Iraq. While this approach has drawn deep and lasting criticism, it is, in fact, in accord with many principles of both military and corporate strategy. In the following paper we explore several models of terrorist networks and the implications of both the models and their substantive conclusions for combating terrorism.Comment: 13 pages, 3 figures. Proceedings of the 2004 annual meeting of the North American Association for Computation in the Social and Organizational Science

Emergent Properties of Terrorist Networks, Percolation and Social Narrative

In this paper, we have initiated an attempt to develop and understand the driving mechanisms that underlie fourth-generation warfare. We have undertaken this from a perspective of endeavoring to understand the drivers of these events from a Complexity perspective by using a threshold-type percolation model. We propose to integrate this strategic level model with tactical level Big Data, behavioral, statistical projections via a fractal operational level model and to construct a hierarchical framework that allows dynamic prediction. Our initial study concentrates on this strategic level, i.e. a percolation model. Our main conclusion from this initial study is that extremist terrorist events are not solely driven by the size of a supporting population within a socio-geographical location but rather a combination of ideological factors that also depends upon the involvement of the host population. This involvement, through the social, political and psychological fabric of society, not only contributes to the active participation of terrorists within society but also directly contributes to and increases the likelihood of the occurrence of terrorist events. Our calculations demonstrate the links between Islamic extremist terrorist events, the ideologies within the Muslim and non-Muslim population that facilitates these terrorist events (such as Anti-Zionism) and anti-Semitic occurrences of violence against the Jewish population. In a future paper, we hope to extend the work undertaken to construct a predictive model and extend our calculations to other forms of terrorism such as Right Wing fundamentalist terrorist events within the USA.Comment: 9th International Conference on Complex Systems, 15 page

Ontological Determinism non-locality and the system problem in quantum mechanics

Wave functions live on configuration space. Schrodinger called this entanglement. The linearity of the Schrodinger equation prevents the wave function from representing reality. If the equation were non-linear (e.g., reduction models) the wave function living on configuration space still by itself could not represent reality in physical space. In this paper, we continue the line of reasoning discussed in our previous paper, "The Fundamental Importance of Discourse in Theoretical Physics", [arXiv:1001.4111], to explore the "measurement problem" in quantum mechanics. In particular we present a new interpretation of quantum decoherence, and a novel critique of the double slit experiment. In addition, we review the use of "determinism" in the discourse of quantum mechanics, resolving the confusion created by theories which attempt to restore determinism to quantum mechanics while confusing determinism with ontological necessity. Finally, we review Bell's Theorem in order to demonstrate that nonlocality is an inherent ontological quality of the configuration space of the universe regardless of deterministic or non-deterministic character of quantum mechanics.Comment: 14 pages, 8th International Conference on Complex System

Time, Uncertainty and Non-Locality in Quantum Cosmology

In this paper we build on our previous work and the work of Peter Lynds within a Bohmian framework to consider the intervallic structure of thermodynamic reversibility as well as presenting new considerations for the measurement of uncertainty at cosmic scales. In addition we address the fundamental nature of non-locality as an underlying element of cosmological structure.Comment: 12 pages; 8th International Conference on Complex System

Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions

In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time ordering, thermodynamic reversibility, singularities and boundary conditions in the formation of the early universe. We briefly reference Smolin and Kauffman's recent arguments with respect to possible processes of "evolutionary selection" in early universe formation as an alternative explanation to key elements of Hawking's earlier "M-Theory", and its attendant anthropic principle. We also briefly excerpt a short section of Smolin's recent work on topology in quantum loop gravity, simply as an illustrative example of the type of complex quantum topological transformation which he offers as a theoretical alternative to string theory in quantum cosmology.Comment: 17 pages, 2 figures. 7th International Conference on Complex System

Ontological Determinism, non-locality, quantum equilibrium and post-quantum mechanics

In this paper, we extend our previous discussion on ontological determinism, non-locality and quantum mechanics to that of the Sarfatti post-quantum mechanics perspective. We examine the nature of quantum equilibrium and non-equilibrium and uncertainty following the Sarfatti description of this theoretical development, which serves to extend the statistical linear unitary quantum mechanics for closed systems to a locally-retrocausal, non-statistical, non-linear, non-unitary theory for open systems. We discuss how the Bohmian quantum potential has a dependence upon the position of its Bell beable and how Complexity mathematics describes the self-organizing feedback between the quantum potential and its beable allowing nonlocal communication.Comment: 9th International Conference on Complex Systems, Cambridge, MA July, 2018 8 page

Disrupting Terrorist Networks, a dynamic fitness landscape approach

Over a period of approximately five years, Pankaj Ghemawat of Harvard Business School and Daniel Levinthal of the Wharton School have been working on a detailed simulation (producing approximately a million fitness landscape graphs) in order to determine optimal patterns of decision-making for corporations. In 2006, we adapted this study, combining it with our own work on terrorism to examine what would happen if we inverted Ghemawat and Levinthal's findings and sought to provide disinformation or otherwise interfere with the communications and decision processes of terrorist organizations in order to optimize poor decision making and inefficiencies in organizational coordination, command and control. The bulk of this study was then presented at the 2006 annual meeting of the North American Association for Computation in the Social and Organizational Sciences. We present here an updated version of that study, emphasizing the rather counter-intuitive finding that "soft" targets have almost no value and that unless one can influence key factors, an effort directed at the easy to reach elements of terrorist organizations may actually be worse than mounting no effort at all. We conclude with the recommendation that some fundamental rethinking may be required if the United States is to effectively defend itself from future terrorist attacks.Comment: 12 pages, 8 figures. Proceedings of the 2006 annual meeting of the North American Association for Computation in the Social and Organizational Science

Dynamic modeling of competing technology designs, pricing and consumer dynamics

The modeling of technology succession and new technology adoption includes a wide array of techniques from complexity theory. In our previous work, we applied the results of the Windrum-Birchenhall model to technology policy and technology development strategies. However, as we began to explore the Windrum-Birchenhall simulation we discovered significant limitations in their model and felt that a new model was needed which could accommodate simultaneous macro and micro-level events in order effectively simulate market volatilities. The following paper discusses the architecture of the new model of technological succession developed at the Southern New Hampshire University International Business Modeling Laboratory and explains results from early simulation runs. We continue to develop this model and expect to have additional applications and simulation results as our research progresses.Comment: 9 pages, 6 figures. Proceedings of the 2006 annual meeting of the North American Association for Computation in the Social and Organizational Science

Adaptation and Coevolution on an Emergent Global Competitive Landscape

Notions of Darwinian selection have been implicit in economic theory for at least sixty years. Richard Nelson and Sidney Winter have argued that while evolutionary thinking was prevalent in prewar economics, the postwar Neoclassical school became almost entirely preoccupied with equilibrium conditions and their mathematical conditions. One of the problems with the economic interpretation of firm selection through competition has been a weak grasp on an incomplete scientific paradigm. As I.F. Price notes, "The biological metaphor has long lurked in the background of management theory largely because the message of 'survival of the fittest' (usually wrongly attributed to Charles Darwin rather than Herbert Spencer) provides a seemingly natural model for market competition (e.g. Alchian 1950, Merrell 1984, Henderson 1989, Moore 1993), without seriously challenging the underlying paradigms of what an organisation is." In this paper we examine the application of dynamic fitness landscape models to economic theory, particularly the theory of technology substitution, drawing on recent work by Kauffman, Arthur, McKelvey, Nelson and Winter, and Windrum and Birchenhall. In particular we use Professor Post's early work with John Holland on the genetic algorithm to explain some of the key differences between static and dynamic approaches to economic modeling.Comment: 16 pages, 5th International Conference on Complex System